Per the rules of Find Familiar, familiars can deliver touch spells on behalf of their owner:
Finally, when you cast a spell with a range of touch, your familiar can deliver the spell as if it had cast the spell. Your familiar must be within 100 feet of you, and it must use its reaction to deliver the spell when you cast it. If the spell requires an attack roll, you use your attack modifier for the roll.
But what if the familiar's owner had previously also cast Hex on the target?
The description for Hex states:
Until the spell ends, you deal an extra 1d6 necrotic damage to the target whenever you hit it with an attack.
Would the touch spell delivered through the familiar also include Hex damage?
While Hex state it happens with "you hit it with an attack", the "hit it" is the familiar delivering the touch spell attack. But by the same token, Find Familiar says that "If the spell requires an attack roll, you use your attack modifier for the roll." So the "hit it" is based on the caster's abilities, not the familiar's.
So when a familiar does the dirty work, who exactly is "hitting it" and can it include Hex damage?
Best Answer
The familiar doesn't cast the spell, hex damage is applied
The rules for Find Familiar state:
Who has cast the spell? 'You' have - this is stated explicitly and the spell uses your attack modifier, not your familiar's. Your familiar has delivered the spell 'as if it had cast it' but it has not actually cast it - 'you' have.
The rules for Hex state:
So in this case, you can deal hex damage as it was you that cast the spell, as your attack.
Your familiar delivering the spell 'as if it had cast' it simply means you can use your familiar's location rather than your own when determining range.